Method for relative lead offset determination

ABSTRACT

A method for estimating an offset between a first group and a second group of contacts with respect to a longitudinal direction. Each group of contacts includes a plurality of electrodes arranged along a surface of a body of a lead. The method includes the steps of: (a) Selecting a number of electrode pairs, each electrode pair including an electrode of the first contact group and an electrode of the second contact group, and measuring the impedances between the electrodes of each selected electrode pair; (b) pre-conditioning the measured impedances for attenuating unwanted noise to generate pre-conditioned impedances, and (c) determining the lead offset using the pre-conditioned impedances.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims the benefit, under 35 U.S.C. § 119(e), ofprovisional patent application No. 62/753,106 filed Oct. 31, 2018; theprior application is herewith incorporated by reference in its entirety.

BACKGROUND OF THE INVENTION Field of the Invention

The present invention relates to a method and a system for estimating alead offset between a first lead and a second lead with respect to alongitudinal direction along which the respective lead extends.

In the field of neuromodulation, particularly in the field ofimplantable neuromodulation devices which comprise multiple electrodesfor contacting tissue to apply neurostimulation that are arranged in anarray with varying positions between groups of electrodes, it isdesirable to identify the relative position of said groups duringimplanting as well as when the electrode leads are already implanted (orduring an operation). A shift in the position of a group of electrodesrelative to another group may impact the effects of an ongoing therapy,indicating a need to adjust the therapy's parameters or re-adjustelectrode position.

Spinal cord stimulation (SCS) leads are implanted in a specific positionand orientation to steer the electrostimulation delivered through one ora combination of multiple electrodes on the electrode leads towardsneural elements in the spinal cord that influence nociception and canalleviate chronic pain. The relative position of the electrode leadswith respect to each other is a critical factor in SCS therapyefficiency: pain relief can be substantially decreased if the electrodeleads shift, which could require electrostimulation reprogramming tocompensate for the offset, or surgical intervention to reposition theleads.

Present processes to determine the position of the leads using medicalimaging, such as radiography and fluoroscopy, entail significant costand time, as the patient has to be examined at the hospital.

Furthermore, it is known in the field to use measurements of electricfields of inactive electrodes induced by activation of other electrodesto deduce electrode lead offset with a minimum finding method. Othermeasurements relate to inter-electrode electric fields and comparisonwith cross-lead field potential profiles generated by reference modelsof the appropriate device geometry and configuration built beforehand,via early measurements at implantation, or computational methods.Furthermore, inter-electrode impedance measurements between all opposingelectrode leads and deduction of electrode lead offset with a minimumfinding method has also been described.

Particularly, U.S. Pat. No. 7,684,869 B2 discloses a method forevaluating electrode lead orientation by calculating monopolar andbipolar impedances between all electrode combinations, calculatingcorrected impedance values in order to generate an impedance map for theelectrode configuration, and determining the electrode combinations withminimum impedance as relatively adjacent electrodes.

Furthermore, U.S. Pat. No. 8,682,447 takes impedance measurementsbetween all inter-lead electrode pairs and may therefore requiresignificant memory capacity and increased battery consumption. Theresolution of the method is one electrode (contact), which preventsusers from detecting lead shifts less than one electrode/contact andreduces the probability of taking effective corrective actions, such as,appropriate electrostimulation reprogramming to compensate for aspecific lead shift based on the detected lead positioning. Furthermore,U.S. Pat. No. 8,682,447 proposes utilizing electric field measurements,and therefore, requires the use of electric currents with sufficientamplitudes to induce measurable electric fields at non-activeelectrodes, though non-perceptible or perceptible but tolerable bysubject, may demand more energy than impedance measurements. Inaddition, the determination of lead shifts is based on a comparison ofthe measured electric fields with a previously saved data set, whichimposes the additional burden of making a lead measurement atimplantation. The solution proposed in U.S. Pat. No. 8,233,992 B2 andothers teach the generation of an electrical profile based on a knownlead staggered configuration, and using that profile along with modelingto estimate electrode positions from a plurality of other cross-leadmeasurements. Electrical profiles generated from electrode sources onSCS leads are however easily influenced by localized tissue properties,and there is a likelihood that the reference electrical profilegenerated from a known staggered lead configuration will not match themeasured lead profile due to tissue inhomogeneity. While this does notpreclude the calculation of a lead offset estimate, it reduces theaccuracy and reliability of said estimate significantly.

Finally, several series of measurements can be required, in order toaccurately determine if the leads have shifted which can requirevariable amounts of memory capacity and may be more energy-consuming.

SUMMARY OF THE INVENTION

Based on the above, it is an object of the present invention to providefor a solution to remotely determine the relative position of theelectrode leads with respect to one another while particularly avoidingexcessive use of the system's memory and significant reduction ofbattery life, and particularly without requiring the patient to undergomedical imaging.

This capability could result in better management of the SCS therapythrough early detection of electrode lead shifts while preservingbattery life.

With the above and other objects in view there is provided, inaccordance with the invention, a method for estimating an offset betweena first and a second group of contacts with respect to a longitudinaldirection or a position of a first group of contacts or second group ofcontacts with respect to a longitudinal direction, is proposed, whereineach group of contacts comprises a plurality of electrodes arrangedalong a surface of a body of a lead, the method comprising the steps of:

(a) selecting a number of electrode pairs, each electrode paircomprising an electrode of the first contact group and an electrode ofthe second contact group, and measuring the Impedances between theelectrodes of each selected electrode pair),

(b) pre-conditioning the measured impedances for attenuating unwantednoise to generate pre-conditioned impedances,

(c) determining said lead offset or position using the pre-conditionedimpedances.

According to the present invention, the proposed method is suitable forestimating an offset between a first and a second group of contacts withrespect to a longitudinal direction or a position of a first group ofcontacts with respect to a second group of contacts with respect to alongitudinal direction. Therefore, the term lead offset is used as asubstitute for lead position in the present application.

According to an embodiment, the first and the second contact group areelectrode contacts of a medical lead.

According to an embodiment, the offset is a positional offset betweentwo medical leads.

According to an embodiment, the present invention is configured todetermine the distance between a multi-electrode lead and a nearbymedium, as for instance the cerebrospinal fluid (CSF).

According to an embodiment, a method for estimating a lead offsetbetween a first and a second lead with respect to a longitudinaldirection, along which the respective lead extends is disclosed, whereineach lead comprises a plurality of electrodes i, j arranged along asurface of a body of the respective lead, and wherein each electrode iof the first lead is aligned with a corresponding electrode j of thesecond lead with respect to the longitudinal direction when said offsetis zero, the method comprising the steps of:

(a) Selecting a number N of electrode pairs (i, j), each electrode pair(i, j) comprising an electrode (i) of the first lead and an electrode(j) of the second lead, and measuring the Impedances Z_(i,j) between theelectrodes (i), (j) of each selected electrode pair (i, j),

(b) pre-conditioning the measured impedances Z_(i,j) to attenuateunwanted noise (e.g. electrode-tissue interface impedance contributionsto the measured impedances) to generate pre-conditioned impedances) by

-   -   automatically calculating for each electrode (j) of the second        lead (200) an average impedance (Z _(j)) from the measured        impedances of the electrode pairs ((i, j)) comprising the        electrode (j) and subtracting the average impedance (Z _(j))        from the measured impedances of the electrode pairs ((i, j))        comprising the electrode (j) to obtain processed impedances        (Z_(i,j)′), and        -   automatically calculating for each electrode (i) of the            first lead (100) an average processed impedance (Z _(ι)′)            from said processed impedances (Z_(i,j)′) of the electrode            pairs ((i, j)) comprising the electrode (i) of the first            lead (100) and subtracting the average processed impedance            (Z _(ι)′) from the processed measured impedances of the            electrode pairs ((i, j)) comprising the electrode (i) of the            first lead (100) to obtain said pre-conditioned impedances            (Z_(i,j)″), and

(c) automatically determining said lead offset using the pre-conditionedimpedances (Z_(i,j)″).

Particularly, the method according to the present invention is capableof determining relative lead position between two (e.g. spinal cordstimulation (SCS)) leads based on a set of impedance measurements. Thisis particularly achieved by measurement refinement via an errorestimation and subtraction process, and particularly a subsequentapplication of one of two specific methods described herein, namely peakdetection and validation, or pattern correlation estimation.

According to an embodiment of the method according to the invention,selecting a number N of electrode pairs is performed such that themeasurement pairs contain a distribution of contact impedance offsetsexpected to be experienced by the leads.

In a specific example embodiment, the disclosed device/method candetermine the relative position in the longitudinal direction of saidleads with a resolution of ¼ electrode and accuracy of ½ electrode.

In the context of the invention, “resolution of one electrode” or “unitof one electrode” refers to the distance formed by the length of anelectrode in longitudinal direction of the lead, plus the space betweentwo electrodes of the first or second lead in the longitudinaldirection. The said distance can alternatively be measured from thecenter of the width of one electrode to the center to the neighboringelectrode in longitudinal direction.

In other words, in order to estimate the relative position of the (e.g.implanted SCS) leads, a series of impedance measurements betweeninter-lead electrode pairs (i, j) is conducted, wherein particularly thechoice of measurements ensures that all electrodes are equally sampledto gather the same amount of information about electrode-specific noise,and that particularly all longitudinal offsets between electrodes of apair cover the desired range of detectable lead offsets to allow leadoffset detection on this range. Further, particularly, pre-conditioningof the measured data set comprises using the distribution ofmeasurements to subtract estimations of electrode-specificcharacteristics and extract the characteristic profile that depends on(represents) electrode-to-electrode distances. Further, particularly,the relative lead longitudinal offset is estimated based on thepre-conditioned impedance data set.

As will be described in more detail below, the step of estimating thelead offset can be carried out by, e.g., two different embodimentswherein according to a first embodiment an integer lead offset isestimated based on the minimum of the pre-conditioned impedance profile,and a fractional lead offset is estimated as well based on the integerlead offset and relative comparison of adjacent data points. The leadoffset is then given by the sum of the integer and the fractionaloffset.

Alternatively, as will be described in more detail below, the leadoffset can be estimated by calculating the correlation coefficient ofthe pre-conditioned impedance profile with a series of leadoffset-specific templates (also denoted as template profiles herein)particularly generated beforehand and, e.g., embedded in the system. Theoffset of the template associated with the largest correlationcoefficient is then assumed to be the representative lead offset. Thetemplates are particularly not patient-specific and can be determinedbefore implantation of the system, using computational simulations ofimpedance profiles based on a database of clinical impedancemeasurements.

Particularly, regarding the present invention, implanting leads into apatient is explicitly not a requisite of the method according to thepresent invention, which aims at estimating lead offset based onmeasured impedance values, and does particularly not comprise anysurgical steps.

According to an embodiment of the method of the present invention, thenumber N of selected electrode pairs is smaller than the number of allpossible electrode pairs formed by an electrode of the first lead and anelectrode of the second lead.

Further, according to an embodiment of the method of the presentinvention, each of the electrodes of the first and the second lead isincluded in the selected electrode pairs.

Further, according to an embodiment of the method of the presentinvention, the electrode pairs are selected such that all electrodeoffsets in the longitudinal direction between an electrode of the firstlead and an electrode of the second lead are represented. Preferably,all possible whole-numbered (positive or negative) electrode offsets arerepresented. As an example: Assuming a first and a second lead, thefirst lead having 8 electrodes (1 . . . 8), the second lead having 8electrodes (9 . . . 16). In case the electrodes are aligned such thatelectrode pairs (1,9), (2,10), (3,11), (4,12), (5,13), (6,14), (7,15)and (8,16) have lead offset 0. Electrode pair (1,16) has an electrodeoffset of −7, while electrode pair (8,9) has an electrode offset of 7.

Furthermore, according to an embodiment of the method of the presentinvention each of the leads comprises 8 electrodes. According to afurther embodiment, the number N of electrode pairs is N=32.Furthermore, according to an embodiment, each of the electrodes of thefirst and the second lead is included in four of the thirty-two selectedelectrode pairs. Furthermore, according to an embodiment the electrodepairs are selected such that all electrode offsets x (with respect tothe longitudinal direction) between an electrode of the first lead andan electrode of the second lead are present in the range from −7 to 7.This range is preferably meant in units of the width of one electrodeplus the space between two electrodes. Alternatively, the range is meantin units of the width of the center of one electrode to the center ofthe neighboring electrode. In either case, e.g., for a lead with 3-mmlong electrodes separated by 4 mm of insulating material(=inter-electrode space), 1 electrode offset unit would correspond to 7mm. Alternatively, for a lead with 2-mm long electrodes and 3-mm longinter-electrode spaces 1 electrode offset unit would translate to =5 mmin this way demonstrating the embodiment is independent of electrodewidth and spacing so long as it is consistent.

Further, according to an embodiment of the method of the presentinvention, the method is adapted to estimate said lead offset with anaccuracy and resolution of less than the width of an electrode plus thespace between two electrodes of the first or second lead in thelongitudinal direction. The width can alternatively be measured from thecenter of one electrode to the center to the neighboring electrode inlongitudinal direction.

Particularly, according to an embodiment, the two leads are spinal cordstimulation leads configured to apply spinal cord stimulation to apatient.

Furthermore, according to an embodiment, the electrodes of each lead areequidistantly spaced in the longitudinal direction.

Furthermore, according to an embodiment, the electrodes of both leadscomprise an identical width in the longitudinal direction.

Furthermore, according to an embodiment, each two neighboring electrodesof the first lead are separated by an electrically isolated section ofthe body of the first lead. Likewise, particularly, each two neighboringelectrodes of the second lead are separated by an electrically isolatedsection of the body of the second lead.

Further, according to an embodiment of the method of the presentinvention, the step of determining said lead offset using thepre-conditioned impedances Z_(i,j)″, comprises calculating for eachconsidered electrode offset x (with respect to the longitudinaldirection) between an electrode of the first lead and an electrode ofthe second lead (e.g. for x=−7 to 7 in units of electrode offset) anaverage impedance value corresponding to an average of thepre-conditioned impedance values for the respective electrode offset x.

Further, according to an embodiment of the method of the presentinvention, the step of determining said lead offset further comprisesnormalizing said average pre-conditioned impedance values that can becollected in a vector Y normalized to the interval [0,1].

Further, according to an embodiment of the method of the presentinvention, the step of determining said lead offset further comprisesfinding a minimum normalized impedance value among said normalizedaverage pre-conditioned impedance values (vector Y), wherein thecorresponding electrode offset corresponds to an integer offset, whereinthe lead offset to be determined is the sum of said integer offset and afractional offset.

Further, according to an embodiment of the method of the presentinvention, determining said fractional offset comprises the furthersteps of extracting the two normalized impedance values corresponding tothe two considered electrode offsets neighboring the minimum impedancevalues.

According to an embodiment, the differences between the normalizedimpedance values adjacent to the minimum normalized impedance value(which is 0 since normalization is made in the [0, 1] interval) arecompared against each other as follows:

-   -   If the smallest value among the two normalized impedance values        adjacent to the minimum normalized impedance value is between 0        and ⅓ (included) of the greatest value among the two normalized        impedance values adjacent to the minimum normalized impedance        value, then it is estimated that the electrode contacts of one        lead are facing the centers of the inter-electrode spaces of the        other lead, which translates into a fractional offset of ±0.50        electrodes.    -   If the smallest value among the two normalized impedance values        adjacent to the minimum normalized impedance value is between ⅓        (excluded) and ⅔ (included) of the greatest value among the two        normalized impedance values adjacent to the minimum normalized        impedance value, then it is estimated that the electrodes of one        lead are facing the middle between the electrodes and the        centers of the inter-electrode spaces of the other lead, which        translates into a fractional offset of ±0.25 electrodes.    -   Finally, if the smallest value among the two normalized        impedance values adjacent to the minimum normalized impedance        value is between ⅔ (excluded) and the greatest value among the        two normalized impedance values adjacent to the minimum        normalized impedance value, then it is estimated that the        electrodes of one lead are facing the electrodes of the other        lead, which translates into a fractional offset of zero        electrodes.

The sign of the fractional offset depends on the considered electrodeoffset of the greatest value among the two normalized impedance valuesadjacent to the minimum normalized impedance value with respect to theinteger offset: if the considered electrode offset of the greatest valueamong the two normalized impedance values adjacent to the minimumnormalized impedance value correspond to an electrode offset greaterthan the integer offset, then the sign of the fractional offset isnegative. Reciprocally, if the considered electrode offset of thegreatest value among the two normalized impedance values adjacent to theminimum normalized impedance value correspond to an electrode offsetless than the integer offset, then the sign of the fractional offset ispositive.

The following paragraph describes an example to illustrate the abovedefinition. If the minimum normalized impedance value z₁ correspond tothe electrode offset +1, then the normalized impedance value z₀ and z₂at electrode offsets 0 and 2, respectively, are collected in a vector Mas follows: [z₀, z₁, z₂]. Say that z₀ is smaller than z₂, then itsrelative value compared to z₁ and z₂ determines the fractional offset asfollows:

if 0≤z₀≤z₂, then the fractional offset is −0.50 electrode;

if ⅓z₂≤z₀←⅔z₂, then the fractional offset is −0.25 electrode;

if ⅔z₂≤z₀≤z₂, then the fractional offset is 0 electrode.

Conversely, if z₂ is smaller than z₀, then its relative value comparedto z₁ and z₀ determines the fractional offset as follows:

if 0≤z₂≤⅓z₀, then the fractional offset is +0.50 electrode;

if ⅓z₂<z₂≤⅔z₀, then the fractional offset is +0.25 electrode;

if ⅔z₂<z₂≤z₀, then the fractional offset is 0 electrode.

The lead offset is therefore the sum of the electrode offset of theminimum impedance value z₁ (integer offset), +1, and the fractionaloffset, 0 in the example given in FIG. 3B, which gives a lead offset of+1 electrode.

See FIG. 3B for a graphical example with the corresponding step-by-stepdeduction of the lead offset to help illustrate the example above.

Note that when the minimum normalized impedance value correspond to aconsidered electrode offset that is one of the boundary of the range ofpossible lead offsets (e.g. −7 or 7 electrodes), then the two adjacentvalues analyzed to calculate the fractional offset are the twonormalized impedance values corresponding to the two consideredelectrode offsets closest to the integer offset (e.g. the normalizedimpedance values corresponding to considered electrode offsets of −6 and−5 electrodes if the integer offset is −7 in units of electrodes).

Further, according to an alternative embodiment of the method of thepresent invention, the step of determining said lead offset using thepre-conditioned impedances Z_(i,j)″, comprises calculating for eachconsidered electrode offset x (with respect to the longitudinaldirection) between an electrode of the first lead and an electrode ofthe second lead (e.g. for x=−7 to 7 in units of electrodes) an averageimpedance value corresponding to an average of the pre-conditionedimpedance values for the respective electrode offset x, and forming apre-conditioned impedance profile, wherein said pre-conditionedimpedance profile comprises said averages of the pre-conditionedimpedance values for the respective electrode offset x, and wherein aplurality of template profiles is provided, wherein each templateprofile corresponds to a detectable lead offset and comprises impedancevalues versus lead offset values, wherein particularly the impedancevalues are taken from in-vivo measurements and/or from one or severalcomputational or in-vitro simulations, and calculating correlationcoefficients between the pre-conditioned impedance profile and all ofthe template profiles, wherein the lead offset is estimated to be thelead offset of the template profile corresponding to the greatestcorrelation coefficient.

With the above and other objects in view there is also provided, inaccordance with the invention, a system for estimating a lead offsetbetween a first and a second lead with respect to a longitudinaldirection, along which the respective lead extends. The systemcomprises:

a first lead and a second lead, particularly extending in parallel alonga longitudinal axis, wherein each lead comprises a plurality ofelectrodes i, j arranged along a surface of a body of the respectivelead,

a measuring unit for measuring Impedances Z_(i,j) between the electrodesi, j of a number of selected electrode pairs (i, j), each electrode pair(i, j) comprising an electrode i of the first lead and an electrode j ofthe second lead,

an analyzing unit configured to pre-condition the measured impedancesZ_(i,j) for attenuating unwanted noise (e.g. electrode-tissue interfaceimpedance contributions to the measured impedances) so to generatepre-conditioned impedances Z_(i,j)″, wherein the analyzing unit isfurther configured to

calculate for each electrode j of the second lead an average impedance Z_(J) from the measured impedances of the electrode pairs (i, j)comprising the electrode j and subtracting the average impedance Z _(J)from the measured impedances of the electrode pairs (i, j) comprisingthe electrode j to obtain processed impedances Z_(i,j)′, and

calculate for each electrode i of the first lead an average processedimpedance Z _(ι)′ from said processed impedances Z_(i,j)′ of theelectrode pairs (i, j) comprising the electrode i of the first lead andsubtracting the average processed impedance Z _(ι)′ from the processedmeasured impedances of the electrode pairs (i, j) comprising theelectrode i of the first lead to obtain said pre-conditioned impedancesZ_(i,j)″, and

determine said lead offset using the pre-conditioned impedancesZ_(i,j)″.

The analyzing unit can be a processing unit on which a suitablealgorithm is executed that receives the measured impedances as an input.

Furthermore, the analyzing unit is configured to conduct the steps ofthe method according to the present invention (e.g. as stated in one ofthe claims 2 to 11).

Further, according to an embodiment, a system comprised of animplantable device, leads, and an external interface is disclosed. Thesystem is capable of determining relative lead position or a lead offsetbetween two spinal cord stimulation leads based on a set of impedancemeasurements, and conveying this to a user. This is achieved by

-   -   1) measurement refinement via an error estimation and        subtraction process,    -   2) subsequent application of one of two disclosed approaches:        peak detection and validation, or pattern correlation estimation    -   3) conveyance of the lead offset information to an end user via        at least one of a variety of user interface means (display,        audio, etc).

According to an embodiment, a system is proposed, comprising animplantable pulse generator (IPG), stimulation leads, and an externalprogrammer device which is in communication with the IPG. The IPG iselectrically connected to the leads and the leads terminate in a seriesof electrodes, designed to provide therapeutic stimulation, for exampleto a patient's spinal cord. The IPG is capable of performing impedancemeasurements between lead electrodes, and transmitting the measurementinformation to the external programmer for analysis which is describedin the following. The external programmer receives impedance measurementinformation and performs calculations as described below to determinethe relative lead offset of the distal (contact) end of the implantedleads, and communicates the end result to the user. In otherembodiments, the IPG may transmit impedance measurements through aserver which may process the data and display the end result on a webpage to an end user. Preferably, the lead position or impedancemeasurements are logged such that the trend over time of lead positionmay be recorded. Furthermore, the lead relative position measurementsmay be triggered and transmitted from the stimulator using a remotesession, and the lead relative offset may then be calculated anddisplayed to a remote user for assessment of the patient leads and toprovide information relevant to stimulation programming and updates.

Other features which are considered as characteristic for the inventionare set forth in the appended claims.

Although the invention is illustrated and described herein as embodiedin a method for relative lead offset determination, it is neverthelessnot intended to be limited to the details shown, since variousmodifications and structural changes may be made therein withoutdeparting from the spirit of the invention and within the scope andrange of equivalents of the claims.

The construction and method of operation of the invention, however,together with additional objects and advantages thereof will be bestunderstood from the following description of specific embodiments whenread in connection with the accompanying drawings.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING

FIG. 1 shows two parallel electrode leads, and the electrical model ofimpedance measurements. Z_(p) represents the electrode-tissue interfaceimpedance of electrode p, and Z_(tissue(q)) represents the impedance ofthe tissue portion that separates two electrodes opposed with alongitudinal offset of q electrodes;

FIG. 2 shows the situation of (a) a non-integer offset where Z″_(2,9)and Z″_(2,10) are theoretically equal and (b) an integer offset whereZ″_(2,9) and Z″_(2,10) are theoretically not equal;

FIG. 3A shows an illustration of lead offset determination using anexample of a normalized impedance profile after the pre-conditioning ofthe data. In this example, the two leads have an offset of +1.00electrode;

FIG. 3B shows examples of step-by-step deduction of the lead offsetaccording to embodiments of the method according to the invention.

FIGS. 4A-4D show examples of lead offset-specific templates superimposedon pre-conditioned subject impedance data sets. The respective leadoffsets of the subject data are FIG. 4A: 0 electrode, FIG. 4B: +0.50electrode, FIG. 4C: +5.50 electrode and FIG. 4D: greater than or equalto +7.00 electrodes.

FIGS. 5A and 5B show a distribution of lead offset estimation errors ofthe method according to the present invention with 5A in-vivo and 5Bcomputationally simulated data. The minimum-based method corresponds toestimations resulting from the use of the method of the minimumimpedance value described herein and the template-based method resultsfrom the use of the method of the best correlating impedance profiletemplate described herein. The grey shades of the bars show thedistribution of errors, from ¼ electrode (contact) to over ½ electrode(contact).

FIG. 6 is a schema illustrating part of the electrical model ofimpedance measurements.

FIG. 7 illustrates the function f used for 8-electrode lead systems,defining tissue impedance (Ztissue) weights versus contact offset.

FIG. 8 shows a spinal cord cross section showing the main structures.

FIG. 9 shows a schematic representation of the coronal plan of thespinal cord.

FIG. 10 illustrates the estimation of the variation of ratio R accordingto lead-to-CSF distance using mathematical equations based on the modelillustrated in FIG. 9 and realistic spinal cord dimensions andconductivities.

FIG. 11 illustrates the estimation of the variation of ratio differencesD according to electrode pair distance, using mathematical equationsbased on the model illustrated in FIG. 9 and realistic spinal corddimensions and conductivities.

FIG. 12 illustrates the impedance measurements matrix Z, filled onlywith the selection of 32 measurements. The dashed rectangle shows thefirst set of values over which the average should be calculated toachieve substep (i) of step (b) of the method according to anembodiment.

DETAILED DESCRIPTION OF THE INVENTION

The present invention is particularly based on the concept thatinter-electrode impedance measurements can be represented by theelectrical model illustrated in FIG. 1 , wherein Z_(p) represents theelectrode-tissue interface impedance of electrode p, and Z_(tissue(q))represents the impedance of the tissue portion that separates twoelectrodes opposed with a longitudinal offset of q electrodes.

FIG. 1 shows a first and a second lead 100, 200 extending in alongitudinal direction z, respectively, wherein each lead 100, 200comprises a plurality of electrodes 1, . . . , 8 and 9, . . . , 16,wherein the electrodes 1, . . . , 8 and 9, . . . , 16 are equidistantlyspaced along a surface 102, 202 of a body 101, 201 of the respectivelead 100, 200 for applying neurostimulation, wherein neighboringelectrodes (e.g. 1 and 2 of lead 100) are separated by an electricallyisolated section 300 of the body 101, 201 of the respective lead 100,200.

Each of the electrodes i, j of the respective lead 100 or 200 areelectrically connected through respective wires, arranged within thebody 101, 201 of the respective lead 100, 200, to an implantable pulsegenerator (not shown), which is configured to apply electricalstimulation to the patient through selected electrodes via thecorresponding wires.

For instance, measuring the impedance between electrode 2 and electrode10 is equivalent to measuring in series the electrode-tissue interfaceimpedance of electrode 2, the bulk impedance of the tissue thatseparates electrode 2 and 10, followed by the electrode-tissue interfaceimpedance of electrode 10.

If the leads 100, 200 are aligned, as is the case in the schema of FIG.1 , the portion of tissue separating electrodes 2 and 9 is larger thanthe portion of tissue separating electrodes 2 and 10, because of thelarger distance between the two electrodes 2 and 9. This larger distanceis characterized by an offset of one electrode between the twoelectrodes 2 and 9, as electrode 9 is just one electrode higher thanelectrode 2 in the longitudinal direction z of the leads 100, 200.

This longitudinal offset between an electrode 1, . . . , 8 of the firstlead 100 and an electrode 9, . . . , 16 of the second lead 200 will alsobe referred to as electrode offset herein and is explicated for eachelectrode pair formed by an electrode 1, . . . , 8 of the first lead 100and an electrode 9, . . . , 16 of the second lead 200 in Table 1.Similarly, in the case of non-aligned leads 100, 200, the relativeposition of the leads 100, 200 is expressed in terms of lead offset, inunits of electrodes.

This unit is preferably meant in the width of one electrode plus thespace between two electrodes. Alternatively, the range is meant in unitsof the width of the center of one electrode to the center of theneighboring electrode. In either case, e.g. a lead with 3-mm longelectrodes separated by 4 mm of insulating material (=inter-electrodespace), that unit would correspond to 7 mm. For a lead with 2-mm longelectrodes and 3-mm long inter-electrode spaces, it would translate intoan offset of 5 mm.

Assuming a lead offset of +1.00 electrode in FIG. 1 would for instanceimply that electrodes 2 and 9 are aligned in FIG. 1 .

TABLE 1 Matrix C of electrode offsets corresponding to impedancemeasurements, assuming lead alignment, in units of electrodes.Electrodes 1 to 8 of first lead 100 are represented by columns 1 to 8and electrodes 9 to 16 of the opposed second lead 200 by rows 9 to 16.Electrode # 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 10 −1 0 1 2 3 4 5 6 11 −2−1 0 1 2 3 4 5 12 −3 −2 −1 0 1 2 3 4 13 −4 −3 −2 −1 0 1 2 3 14 −5 −4 −3−2 −1 0 1 2 15 −6 −5 −4 −3 −2 −1 0 1 16 −7 −6 −5 −4 −3 −2 −1 0

The contribution of electrode-tissue interface impedance components inmeasured inter-electrode impedances is significantly greater thantissue-related impedance components, although it is the latter thatholds information about leads positions. Particularly, the meansaccording to the present invention attenuates the former factor andextracting the relevant impedance components allowing for lead offsetdetermination.

In the following an embodiment of the method according to the presentinvention will be explained for two leads 100, 200, wherein each leadcomprises 8 electrodes. The method however, also applies to an arbitrarynumber of electrodes of the leads.

Particularly, according to an embodiment, the method according to thepresent invention comprises the steps of:

-   -   (a) Measure the impedance of a specific selection of 32        electrode pairs between the two opposing leads 100, 200.    -   (b) Pre-condition the collected 32 impedance measurements data        set.    -   (c) Determine the relative lead longitudinal offset based on the        pre-conditioned impedance data set.

Further, according to an embodiment, the third step (c) can be carriedout according to two alternative embodiments, namely by means of amethod of the minimum impedance value, or by means of a method of thebest correlating impedance profile template.

Embodiments and particulars of the three steps (a), (b), and (c) aredescribed in more detail below.

Particularly, measuring the impedance of a specific selection of 32electrode pairs between the two opposing leads 100, 200 in step (a), asshown on FIG. 1 comprises in an embodiment that the chosen measurementsare specifically distributed among all of the 64 possible combinationsto allow for(1) each of the electrodes 1, . . . , 8 and 9, . . . , 16 to be includedin four selected electrode pairs, and(2) represent all possible longitudinal electrode offsets between anelectrode of the first lead 100 and an electrode of the second lead 200.

To illustrate point (1), electrode 1—represented by column 1 in Table2—is used in four different measurements: it is part of the selectedelectrode pairs (1, 10), (1, 12), (1, 14) and (1, 16) as indicated inTable 2. By equally distributing the measurements between all electrodesin such a way that each electrode is sampled in the same number ofmeasurements, information about all of the 64 electrode-tissue interfaceimpedances is equally acquired, that is then used to attenuate theirweight in the following pre-conditioning step (b).

Further, point (2) refers to the longitudinal offset that can existbetween two electrodes of two aligned leads 100, 200, reported for eachelectrode pair in Table 1. For instance, the offset between the selectedpair of electrodes (7,9) and (1,16) is +6 and −7 electrodes,respectively. The 32 selected impedance measurements shown in Table 2corresponds to offsets of −7 to +7 electrodes (shown in Table 1), whichis a preferred requirement to allow for accurate lead offsetdetermination.

TABLE 2 Table showing the distribution of the selected 32 measurementsamong the possible electrodes combinations. Electrodes 1 to 8 of firstlead 100 are represented by columns 1 to 8 and electrodes 9 to 16 of theopposed second lead 200 by rows 9 to 16. Z_(i, j), i ∈{1, . . . , 8}, j∈{9, . . . , 16} represents the impedance measured between electrodes iand j. Electrode # 1 2 3 4 5 6 7 8 9 Z_(3, 9)   Z_(4, 9)   Z_(7, 9)  Z_(8, 9)   10 Z_(1, 10) Z_(2, 10) Z_(5, 10) Z_(6, 10) 11 Z_(3, 11)Z_(4, 11) Z_(7, 11) Z_(8, 11) 12 Z_(1, 12) Z_(2, 12) Z_(5, 12) Z_(6, 12)13 Z_(3, 13) Z_(4, 13) Z_(7, 13) Z_(8, 13) 14 Z_(1, 14) Z_(2, 14)Z_(5, 14) Z_(6, 14) 15 Z_(3, 15) Z_(4, 15) Z_(7, 15) Z_(8, 15) 16Z_(1, 16) Z_(2, 16) Z_(5, 16) Z_(6, 16)Considering that electrode-tissue interface impedances are part ofunwanted noise, the pre-conditioning of the collected impedance data setaims at significantly increasing the signal-to-noise ratio byattenuating the electrode-specific impedance component Z_(i,j) from themeasured values (Z_(i,j), i∈{1, . . . , 8}, j ∈{9, . . . , 16}) bysequentially subtracting the average impedance of each electrode, sothat an approximation of only the electrode offset-dependent componentsZ_(tissue(q)), q∈{−7, . . . , 7}, remain and can be exploited todetermine the lead offset.

According to an embodiment, this pre-conditioning of data particularlycomprises the steps described in the following:

-   -   (i) Calculate the average Z₉ of the values in the dashed        rectangle of Table 3, omitting the empty cells.

FIG. 12 shows impedance measurements matrix Z, filled only with theselection of 32 measurements. The dashed rectangle shows the first setof values over which the average should be calculated to achieve substep(i) of step (b) of the method according to an embodiment.

(ii) subtract this average Z ₉ from each value of the dashed rectangle,ignoring empty cells, as shown in Table 4.

TABLE 4 Impedance measurements matrix Z for achieving substep (ii) ofstep (b) of the method according to the present invention. Electrode # 12 3 4 5 6 7 8 9 Z_(3, 9)   − Z_(4, 9)   − Z_(7, 9)   − Z_(8, 9)   − Z₉Z₉ Z₉ Z₉ 10 Z_(1, 10) Z_(2, 10) Z_(5, 10) Z_(6, 10) 11 Z_(3, 11)Z_(4, 11) Z_(7, 11) Z_(8, 11) 12 Z_(1, 12) Z_(2, 12) Z_(5, 12) Z_(6, 12)13 Z_(3, 13) Z_(4, 13) Z_(7, 13) Z_(8, 13) 14 Z_(1, 14) Z_(2, 14)Z_(5, 14) Z_(6, 14) 15 Z_(3, 15) Z_(4, 15) Z_(7, 15) Z_(8, 15) 16Z_(1, 16) Z_(2, 16) Z_(5, 16) Z_(6, 16)

-   -   (iii) repeat substeps (i) and (ii) for each row of Table 3, i.e.        for electrodes 9 to 16. The result is a new matrix Z′ presented        in Table 5.

TABLE 5 Impedance measurements matrix Z′ after executing substep (iii)of step (b) of the method. Electrode # 1 2 3 4 5 6 7 8 9 Z_(3, 9) −Z_(4, 9) − Z_(7, 9) − Z_(8, 9) − Z₉ Z₉ Z₉ Z₉ 10 Z_(1, 10) − Z_(2, 10) −Z_(5, 10) − Z_(6, 10) − Z₁₀ Z₁₀ Z₁₀ Z₁₀ 11 Z_(3, 11) − Z_(4, 11) −Z_(7, 11) − Z_(8, 11) − Z₁₁ Z₁₁ Z₁₁ Z₁₁ 12 Z_(1, 12) − Z_(2, 12) −Z_(5, 12) − Z_(6, 12) − Z₁₂ Z₁₂ Z₁₂ Z₁₂ 13 Z_(3, 13) − Z_(4, 13) −Z_(7, 13) − Z_(8, 13) − Z₁₃ Z₁₃ Z₁₃ Z₁₃ 14 Z_(1, 14) − Z_(2, 14) −Z_(5, 14) − Z_(6, 14) − Z₁₄ Z₁₄ Z₁₄ Z₁₄ 15 Z_(3, 15) − Z_(4, 15) −Z_(7, 15) − Z_(8, 15) − Z₁₅ Z₁₅ Z₁₅ Z₁₅ 16 Z_(1, 16) − Z_(2, 16) −Z_(5, 16) − Z_(6, 16) − Z₁₆ Z₁₆ Z₁₆ Z₁₆

-   -   (iv) starting with Z′, repeat substeps (i) through (iii) of        step (b) of the method but for each column of Table 5. The        resulting matrix Z″ is presented in Table 6.

The impedance matrix Z″ in Table 6 represents the pre-conditionedimpedance data with attenuated electrode-tissue interface impedancecomponents. The remaining impedances are driven by tissue-relatedimpedance components that are dependent on the distance betweenelectrodes of opposed leads and can therefore be analyzed to determinethe relative position of the leads.

TABLE 6 resulting matrix Z″ Electrode # 1 2 3 4 5 6 7 8 9 Z_(3, 9) −Z_(4, 9) − Z_(7, 9) − Z_(8, 9) − Z₉ − Z₉ − Z₉ − Z₉ − Z′₃ Z′₄ Z′₇ Z′₈ 10Z_(1, 10) − Z_(2, 10) − Z_(5, 10) − Z_(6, 10) − Z₁₀ − Z₁₀ − Z₁₀ − Z₁₀ −Z′₁ Z′₂ Z′₅ Z′₆ 11 Z_(3, 11) − Z_(4, 11) − Z_(7, 11) − Z_(8, 11) − Z₁₁ −Z₁₁ − Z₁₁ − Z₁₁ − Z′₃ Z′₄ Z′₇ Z′₈ 12 Z_(1, 12) − Z_(2, 12) − Z_(5, 12) −Z_(6, 12) − Z₁₂ − Z₁₂ − Z₁₂ − Z₁₂ − Z′₁ Z′₂ Z′₅ Z′₆ 13 Z_(3, 13) −Z_(4, 13) − Z_(7, 13) − Z_(8, 13) − Z₁₃ − Z₁₃ − Z₁₃ − Z₁₃ − Z′₃ Z′₄ Z′₇Z′₈ 14 Z_(1, 14) − Z_(2, 14) − Z_(5, 14) − Z_(6, 14) − Z₁₄ − Z₁₄ Z₁₄ −Z₁₄ − Z′₁ Z′₂ Z′₅ Z′₆ 15 Z_(3, 15) − Z_(4, 15) − Z_(7, 15) − Z_(8, 15) −Z₁₅ − Z₁₅ − Z₁₅ − Z₁₅ − Z′₃ Z′₄ Z′₇ Z′₈ 16 Z_(1, 16) − Z_(2, 16) −Z_(5, 16) − Z_(6, 16) − Z₁₆ − Z₁₆ − Z₁₆ − Z₁₆ − Z′₁ Z′₂ Z′₅ Z′₆

Furthermore, according to an embodiment of the method according thepresent invention, step (c) of the method comprises determining the leadoffset between the leads 100, 200 based on the pre-conditioned set ofthe specifically-selected 32 impedance measurements.

Particularly, two embodiments for achieving this task are explained inthe following.

According to a first embodiment a minimum impedance value method can beused to estimate the lead offset.

This embodiment is based on the postulate supported by subjectobservation that if the leads 100, 200 have a non-integer relativeoffset (e.g. every electrode 1, . . . , 8 of a lead 100 is facing anelectrically isolated section 300 of the body of the other lead 200),then the impedance measured between this electrode (e.g. 2) and the twoelectrodes (e.g. 9 and 10) of the opposite lead 200 that are arranged onboth sides of the adjacent section 300 are similar, as indicated in FIG.2(A). On the other hand, in case of an integer offset as shown in FIG.2(B), Z″_(2,9) and Z″_(2,10) are theoretically not equal.

According to an embodiment, a non-integer offset can be as small as ¼electrode offset.

Particularly, according an embodiment, the following steps can beconducted to determine the lead offset:

-   -   For each electrode offset x from −7 to 7 [electrodes], calculate        the average of impedance values measured from electrode pairs        that have an electrode offset of x (see Table 1) and are        pre-conditioned as described above, wherein the corresponding        values are mathematically expressed in Table 6 above. These        average values are stored in a vector Y.    -   Normalize the data in Y to the interval [0, 1].    -   Find the minimum impedance value of vector Y and its        corresponding electrode offset in Table 1: the latter is the        integer offset (the lead offset being the sum of the integer        offset and a fractional offset determined below),    -   Find the impedance values in Y and their corresponding electrode        offsets in Table 1 that are adjacent to the minimum (if the        minimum is located on an extremity of the electrode offset        range, take the impedance values of the two closest electrode        offsets), and store them sequentially in a vector M=[left        adjacent value, minimum value, right adjacent value].        Alternatively, vector M can be described as M=[value        corresponding to electrode offset    -   Compute the first and second difference of the vector M.    -   While the integer offset is indicated by the abscissa of the        square in FIG. 3A (+1.00 electrode), the fractional offset is        determined by the relative value of the minimum between the two        data points adjacent to the square (represented by the circle in        FIG. 3A) with respect to the maximum between the two data points        adjacent to the square (represented by the triangle in FIG. 3A).        The calculated fractional offset can be 0, ±0.25 or ±0.50        electrode, with a negative sign if the circle (smaller value) is        on the left, and a positive sign if it is on the right. The        total lead offset to determine is the sum of the integer and        fractional offset.

In other words, the comparison of the first and second difference ofvector M determines the fractional offset: if the absolute value of thesecond difference is inferior to ⅓ of the maximum of the firstdifferential (i.e. if the circle is in the upper interval in FIG. 3A),then the fractional offset is 0 electrode. If it is between ⅓ and ⅔ ofthe maximum of the first differential (i.e. the circle is in the middleinterval in FIG. 3A), then the factional offset is ±0.25 electrode. Ifit is between ⅔ and 3/3 (i.e. the circle is in the lower interval inFIG. 3A), then the ‘fractional’ offset is ±0.50. The sign of thefractional offset is determined by the relative position of the secondminimum value among the two data points adjacent to the minimum value:the sign is negative if the second minimum corresponds to an electrodeoffset smaller than the integer offset (e.g. circle in FIG. 3A), andpositive if it corresponds to an electrode offset greater than theinteger offset.

FIG. 3B shows examples of step-by-step deduction of the lead offsetaccording to embodiments of the method according to the invention.Depicted is a diagram 300 with Contact offset −8 to 8 along x-axis 301,and normalized impedance along y-axis 302. Graph 306 shows thenormalized impedances after withdrawing electrode-specific impedancesaccording to aspects of the inventive method. According to the example,the point of minimum impedance 303 is measured at contact leadoffset=positive whole-number offset of +1.00. According to an embodimentof the invention, the lead offset can be in this case estimated from+0.50 to +1.50 contacts depending on the adjacent values' relativeposition. Point 304 corresponds to the minimum impedance among the twopoints 304 and 305 adjacent to 303. Point 304 is between ⅔ and 3/3 ofthe maximum adjacent impedance value (point 305). Therefore, in thiscase the fractional offset equals 0 according to embodiments of theinvention, resulting in that the overall lead offset equals +1.00(positive whole-number offset) minus 0 (fractional offset)=+1.00 unit ofelectrodes.

According to an alternative embodiment, a method of the best correlatingimpedance profile template is employed to extract the overall leadoffset.

This embodiment is based on the best correlation of the pre-conditionedimpedance profile, i.e. the graph representing impedance versuselectrode offset after pre-conditioning using the technique describedabove (cf. Table 6), with a lead offset-specific template (also denotedas template profile).

For each possible lead offset, the corresponding template profile can begenerated by averaging a large number of impedance data sets collectedfrom SCS leads used in-vivo or in-vitro or computationally simulatedimpedance data sets if experimental data is lacking or insufficient. Thenumber of templates to generate depends on the maximum range ofdetectable lead offsets (−7 to 7 [electrodes] for 8-electrode leads) andon the measurement resolution (i.e. the smallest difference between twodifferent lead offsets), which is 0.25 electrodes in this specificembodiment.

Particularly, this embodiment comprises the steps of:

-   -   i. calculating the correlation coefficient between the        pre-conditioned impedance profile and all of the lead        offset-specific templates (template profiles), and    -   ii. noting the lead offset of the template profile corresponding        to the greatest correlation coefficient.

Alternately, this embodiment, comprises the steps of:

-   -   i. calculating the correlation coefficient between the        pre-conditioned impedance profile and a set of representative        lead offset-specific templates that do not correspond to all        potential lead offsets (template profiles)    -   ii. additionally calculating the correlation coefficient between        the pre-conditioned impedance profile and mathematical        modifications to lead offset-specific templates which represent        a set of templates corresponding to offsets at a finer        resolution than the stored set of lead offset-specific        templates, and    -   iii. noting the lead offset of the template profile        corresponding to the greatest correlation coefficient.

Particularly, the template profiles are generated via extensivecomputational simulations at each positive lead offset that can bedetected (e.g. from 0 to +7 electrodes with a step of 0.25 electrodes)and are mirrored to generate the negative portion of possible leadoffsets (e.g. from −7 to 0 electrodes with a step of 0.25 electrodes)and thus save memory use. The number of templates to be generated istherefore particularly dependent on the resolution: it is equal to thedifference between the maximum and minimum of the detectable positivelead offset range divided by the resolution, plus one (e.g., 29templates for a positive range of 0 to 7 electrodes and a resolution of0.25 electrodes). The templates are generated beforehand and they can bestored in a device ROM saving working memory.

To illustrate the process, four subject impedance data sets superimposedwith their respective best correlating template, are shown on FIG. 4 .Here, the respective lead offsets of the subject data are FIG. 4A 0.00electrode, FIG. 4B +0.50 electrode, FIG. 4C +5.50 electrodes and FIG. 4Dsuperior or equal to +7.00 electrodes.

The method according to the present invention presents several technicaladvantages compared to known solutions. As an example, with a minimum ofjudiciously selected 32 measurements between two implanted 8-electrodeleads, the present invention allows for estimation of the offset thatcan exist between the leads, with

-   -   a resolution of 0.25 electrodes (one electrode unit is the        length of an electrode in longitudinal direction of lead plus        the distance between the edges of two adjacent electrodes).    -   an accuracy of 0.50 electrodes, which can help for early        detection of lead migration and shifts smaller than 1 electrode.    -   an allocated memory capacity of the system of only 32        measurements in the present example of 8-electrode leads.    -   an independent estimation of the leads relative position without        the need of an initial application at implantation to compare to        subsequent applications of the method.    -   the possibility of remotely performing lead offset determination        without requiring hospital facilities or a patient's visit to a        hospital, which can help taking appropriate corrective actions,        whether it is a reprogramming of the electrostimulation        configuration with respect to the estimated lead migration, or a        surgical repositioning of the leads.    -   the requirement of only an impedance measurement feature (common        to many implantable medical devices) to carry out the method        according to the present invention.    -   At least half the energy consumption compared to techniques that        require impedance measurements between all electrodes.    -   the relative simplicity to implement the overall method, of        which the second (a) and third (c) step can be carried out        outside the implanted system to limit further battery        consumption.

According to an embodiment, the data generated according to theinvention regarding lead offset may be transmitted to an external deviceand/or data center for further processing, analysis based on automatedalgorithms or by the user. Moreover, said data and results from dataprocessing and analysis may be provided to the user (e.g. the physicianor the nurse).

Furthermore, to illustrate the performance of the present invention withrespect to the technical advantages, distributions of estimation errorswere calculated using subject data and computationally simulated data.Subject data consisted of 21 impedance data sets from acuteimplantations of SCS leads, with lead offsets from 0 to +8 electrodesand lead separations from approximatively 1.5 to 5 mm. Simulated dataconsisted of 2,000 simulations of subject data-based realistic impedancedata sets with 0-centered normally distributed lead offsets from −8 to+8 electrodes and uniformly distributed lead separations from 1 to 5 mm.The results are plotted in FIG. 4 , which show that there was noestimation error greater than the expected accuracy of ½ electrodes(contacts) both with subject and simulated data.

FIG. 6 shows a schema illustrating part of the electrical model ofimpedance measurements. Zi represents the electrode-tissue interfaceimpedance of electrode i, and Ztissue(j) represents the impedance of thetissue portion that separates two electrodes opposed with a longitudinaloffset of j contacts.

An embodiment of the invention is based on the concept thatinter-electrode impedance measurements can be represented by theelectrical model illustrated in FIG. 6 . Referring to FIG. 6 , forinstance, measuring the impedance between electrode 2 and electrode 6 isequivalent to measuring in series the electrode-tissue interfaceimpedance of electrode 2, the bulk impedance of the tissue thatseparates electrode 2 and 6, followed by the electrode-tissue interfaceimpedance of electrode 6.

If the leads are aligned, the case in the schema of FIG. 6 , the portionof tissue separating electrode 2 and 5 is larger than the portion oftissue separating electrode 2 and 6, because of the larger distancebetween the two electrodes. This larger distance is characterized by anoffset of 1 contact between the two contacts, as electrode 5 is just onecontact higher than electrode 6 in the longitudinal direction. Thispairwise electrode longitudinal offset will be referred to by “contactoffset” in the rest of this description, and is explicated for eachelectrode pair in Table 7. Similarly, in the case of non-aligned leads,the relative position of the leads is expressed in terms of lead offset,in units of contacts. A lead offset of +1 contact would for instanceimply that electrode 2 and 5 are aligned.

TABLE 7 Matrix C of contact offsets corresponding to impedancemeasurements, assuming lead alignment, in units of contacts. Electrodes1 to 4 of one lead are represented by columns 1 to 4 and electrodes 5 to8 of the opposed lead by rows 5 to 8 Electrode # 1 2 3 4 5 0 1 2 3 6 −10 1 2 7 −2 −1 0 1 8 −3 −2 −1 0

There are two main steps to carry out the first embodiment, and one tocarry out the second embodiment.

-   -   Embodiment 1        -   Impedance pre-conditioning: identify in those measurements            the impedance values of electrode-tissue interfaces and lead            offset-related components.        -   Lead offset determination: apply the minimum finding method            to the pre-conditioned impedance values to find the lead            offset.    -   Embodiment 2: using a contact offset-dependent weigh function.

The two embodiments are described in detail below.

Embodiment 1

A. Impedance Pre-Conditioning

The weight of electrode-tissue interface impedance components inmeasured inter-electrode impedances is significantly heavier thantissue-related impedance components, although it is the latter thatholds information about leads positions. The present invention's firstand second feature thus aims at attenuating this factor and extractingthe relevant impedance components to allow for lead offset determinationin the third invention feature.

The method consists of defining N=(4*n−1) variables, with n the numberof electrodes per lead, describing the impedance structure of the dualleads. For 8-electrode leads, that would be 31 variables. For4-electrode leads, which are used for simplification in this embodiment,that number would be 15. Those variables break down as follows: 8variables represent the electrode-tissue interface impedance Zn of eachelectrode n, and 1 variable Ztissue represents the impedance of thetissue between two opposite electrodes. The tissue impedance between twoelectrodes that are not facing each other is calculated with a functionof the contact difference (the contact offset of the pair (electrode 2,electrode 5) of the example model in FIG. 6 is 1 contact).

Based on this model, a number of equations can be written using thevariables described above and all possible inter-lead impedancemeasurements (64 in case of 8-electrode leads, 16 in case of 4-electrodeleads). For instance, the impedance measured between electrode 2 andelectrode 5 (Z_(2,5)) of the model in FIG. 6 can be described by thefollowing equation:Z ₂ +Z _(tissue(1)) +Z ₅ =Z _(2,5)Similarly, the equation associated to the impedance measure betweenelectrode 2 and 6 (Z_(2,6)) is:Z ₂ +Z _(tissue(0)) +Z ₆ =Z _(2,6)

Note that the number of actual impedance measurements can be lower thanthe number of possible measurements. In fact, the minimum number ofrequired impedance measurements is equal to the number of definedvariables N, that is 31 in case of 8-electrode leads or 15 in case of4-electrode leads. But the greater the number of impedance measurements,the more performant the method. In the current embodiment of 4-electrodeleads, 16 impedance measurements are taken.

Given the 16 impedance measurements available, 16 equations can bewritten the same way. It gives the following system of equations:

$\quad\left\{ \begin{matrix}{{Z_{1} + Z_{{tissue}{(0)}} + Z_{5}} = Z_{1,5}} \\{{Z_{1} + Z_{{tissue}{({- 1})}} + Z_{6}} = Z_{1,6}} \\\vdots \\{{Z_{4} + Z_{{tissue}{(0)}} + Z_{8}} = Z_{4,8}}\end{matrix} \right.$

This can be written as a matrix product, without changing the meaning ofthe equations:

${\begin{pmatrix}1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 \\0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\0 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 \\0 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 \\0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\0 & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0\end{pmatrix}\begin{pmatrix}Z_{1} \\Z_{2} \\Z_{3} \\Z_{4} \\Z_{5} \\Z_{6} \\Z_{7} \\Z_{8} \\Z_{{tissue}{({- 3})}} \\Z_{{tissue}{({- 2})}} \\Z_{{tissue}{({- 1})}} \\Z_{{tissue}{(0)}} \\Z_{{tissue}{(1)}} \\Z_{{tissue}{(2)}} \\Z_{{tissue}{(3)}} \\0\end{pmatrix}} = \begin{pmatrix}Z_{1,5} \\Z_{1,6} \\Z_{1,7} \\Z_{1,8} \\Z_{2,5} \\Z_{2,6} \\Z_{2,7} \\Z_{2,8} \\Z_{3,5} \\Z_{3,6} \\Z_{3,7} \\Z_{3,8} \\Z_{4,5} \\Z_{4,6} \\Z_{4,7} \\Z_{4,8}\end{pmatrix}$

Which can also be written as:

$\begin{matrix}{{{AX} = B}{{With}\text{:}}} & (1) \\{{A = \begin{pmatrix}1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 \\0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\0 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 \\0 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 \\0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\0 & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0\end{pmatrix}},} & \; \\{{X = \begin{pmatrix}Z_{1} \\Z_{2} \\Z_{3} \\Z_{4} \\Z_{5} \\Z_{6} \\Z_{7} \\Z_{8} \\Z_{{tissue}{({- 3})}} \\Z_{{tissue}{({- 2})}} \\Z_{{tissue}{({- 1})}} \\Z_{{tissue}{(0)}} \\Z_{{tissue}{(1)}} \\Z_{{tissue}{(2)}} \\Z_{{tissue}{(3)}} \\0\end{pmatrix}},{B = \begin{pmatrix}Z_{1,5} \\Z_{1,6} \\Z_{1,7} \\Z_{1,8} \\Z_{2,5} \\Z_{2,6} \\Z_{2,7} \\Z_{2,8} \\Z_{3,5} \\Z_{3,6} \\Z_{3,7} \\Z_{3,8} \\Z_{4,5} \\Z_{4,6} \\Z_{4,7} \\Z_{4,8}\end{pmatrix}}} & \;\end{matrix}$

The unknown variables being contained in X, it can be computed by asimple equation rearrangement:AX=B

A ⁻¹ AX=A ⁻¹ B

X=A ⁻¹ B  (2)Thus, X contains each of the electrode-specific impedances and each ofthe contact offset-dependent tissue components. The latter contains theinformation about the actual lead offset.B. Lead Offset Determination

The method of minimum finding is applied using the pre-conditionedZ_(tissue) terms as follows:

-   -   A. Store each Z_(tissue) value in a vector Y in present order of        contact offset (i.e from contact offsets −3 to +3) such as        Y=[Z_(tissue(−3)), . . . , Z_(tissue(3))].    -   B. Normalize the data in Y to the interval [0 1].    -   C. Find the minimum impedance value of vector Y and its        corresponding contact offset in Table 7: the latter is the        ‘integer’ offset.    -   D. Find the impedance values in Y and their corresponding        contact offsets in Table 7 that are adjacent to the minimum (if        the minimum is located on an extremity of the contact offset        range, take the two closest impedance values).    -   E. Compute the first and second difference of the vector M:        [left adjacent value, minimum value, right adjacent value].    -   F. As shown on FIG. 3A, the comparison of the first and second        difference of vector M determines the ‘fractional’ offset: if        the absolute value of the second difference is inferior to ⅓ the        maximum of the first difference (i.e. if the circle is in the        upper interval in FIG. 3A), then the ‘fractional’ offset is 0.        If it is between ⅓ and ⅔ of the maximum of the first difference        (i.e. the circle is in the middle interval in FIG. 3A), then the        ‘fractional’ offset is ¼ contact. If it is between ⅔ and 3/3        (i.e. the circle is in the lower interval in FIG. 3A), then the        ‘fractional’ offset is ½. The sign of the fractional offset is        determined by the relative position of the second minimum value        among the two data points adjacent to the minimum value: the        sign is negative if the second minimum is on the left of the        minimum (e.g. circle in FIG. 3A), and positive if it is on its        right.    -   G. The overall contact offset calculated is the sum of the        ‘integer’ and ‘fractional’ offset.

Embodiment 2

Using a Minimum of (2*n+1) Impedance Measurements (with n Electrodes PerLead)

Embodiment 2 is the same as embodiment 1 except that all of theZ_(tissue(−3)), . . . , Z_(tissue(+3)) terms are reduced to one termZ_(tissue). Each tissue component of the impedance model is representedby a function of the contact offset and Z_(tissue) such as:Z _(i) +f(x)*Z _(tissue) +Z _(j) =Z _(i,j)With i the electrode number of the first lead, j the electrode number ofthe second lead, and x the absolute value of the contact offset (x=1, .. . , 3 with a 4-electrode lead system).

The matrix equations A, X and B from embodiment 1 become:

$\begin{pmatrix}1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & {f(1)} & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & {f(2)} & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & {f(3)} & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & {f(1)} & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & {f(2)} & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & {f(3)} & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & {f(1)} & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & {f(2)} & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & {f(3)} & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & {f(1)} & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & {f(2)} & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 1 & 0 & 0 & 0 & 1 & {f(3)} & 0 & 0 & 0 & 0 & 0 & 0 & 0\end{pmatrix},{X = \begin{pmatrix}Z_{1} \\Z_{2} \\Z_{3} \\Z_{4} \\Z_{5} \\Z_{6} \\Z_{7} \\Z_{8} \\Z_{tissue} \\0 \\0 \\0 \\0 \\0 \\0 \\0\end{pmatrix}},{B = \begin{pmatrix}Z_{1,5} \\Z_{1,6} \\Z_{1,7} \\Z_{1,8} \\Z_{2,5} \\Z_{2,6} \\Z_{2,7} \\Z_{2,8} \\Z_{3,5} \\Z_{3,6} \\Z_{3,7} \\Z_{3,8} \\Z_{4,5} \\Z_{4,6} \\Z_{4,7} \\Z_{4,8}\end{pmatrix}}$

A crucial element of this method is the definition of the function f. Itmust represent the impedance variations with the distance that separatestwo contacts. This function f takes the form of a vector filled withweights for a range of contact offset. It is interpolated over thedesired set of contact offsets. See the example for an 8-electrode leadsystem in

The weight function f requires the assumption of a specific lead offset.For instance, FIG. 7 represents the weight function in case of alignedleads (the minimum impedance is at contact offset 0). To determine thelead offset that should be used for the weight function, i.e. todetermine the actual lead offset, each contact offset is assumed. Foreach assumed contact offset, the function f is calculated, vector X iscalculated, and X is used again to reconstruct the initial impedancematrix B′ and is compared to the real initial matrix B. The assumedcontact offset that results in the minimal error between B and B′ is thelead offset. The steps are broken down as follows:

-   -   a) Assume a contact offset x.    -   b) Build the corresponding weight function f according to the        assumed x.    -   c) Compute the 9 unknown variables in X using X=A⁻¹B (B is the        vector containing the actual impedance measurements)

These 9 unknown variables represent each electrode-specific impedanceplus the tissue impedance. Those electrode-specific impedances can beused independently from the rest of the lead offset algorithm to provideinformation to an end user or unit for other purposes than calculatingthe lead offset, such as, for example:

-   -   A. Provide an end user or unit/system with information about the        integrity of each electrode.    -   B. Provide an end user with an estimated value of electrode        impedance that can be used to track impedance change over time        or unusually high impedance that can impair therapy efficacy.    -   C. Provide an end unit/system with electrode-specific impedance        in order to calculate the maximum current limit of a given        electrode configuration that uses one or multiple electrodes        before the therapy is turned on and thus ensure stimulation        safety.    -   D. Reconstruct the initial impedance matrix B′ using the 9        computed variables (stored in vector X) and AX=B.    -   E. Calculate the root mean square error (RMSE) between the        original and reconstructed impedance matrices B and B′.    -   F. Repeat 1. through 5. for each contact offset assumption x        (from −3 contact to 3 contacts with a step of 0.5).    -   G. Define the actual lead offset as the lead offset assumption        that resulted in the minimum RMSE.

Moreover, multi-electrode leads implanted in the human body usuallyrequire positioning in a medium close to the therapy target to deliverelectrical stimulation. In many neurostimulation applications, thestimulation current must cross both a resistive tissue portion such asfatty tissue and a conductive fluid such as blood or the cerebrospinalfluid in order to reach target excitable cells, for example the spinalcord. The position of the electrodes with respect to one of the portionsis an important factor of the efficiency and success of these therapies,but there is usually little knowledge of that relative positionfollowing implant. Having access to that information can provide newinsights into therapy's outcomes and could shed light on the importanceof a neglected parameter of electrical stimulation therapies, andparticularly in neuromodulation.

According to an embodiment of the present invention, a method and devicefor estimating the proximity of a multi-electrode lead to a localconductivity discontinuity are disclosed. Currently, no solution isknown for such subject. In case of large lead-to-fluid distance (e.g.SCS lead-to-CSF distance), not having any sense of the distance betweenthe lead and the fluid medium prevents from taking corrective action toreduce this distance, which can result in nonoptimal therapy or therapyfailure.

The objective of this invention is to provide information on thedistance between a lead implanted in a medium M1 (e.g. fatty tissue) anda nearby medium M2 (e.g. cerebrospinal fluid, blood), where M1 has asignificantly different conductivity than M2. Benefits from thatinformation include ability to inform therapy adjustment, correction ofthe implant position, optimization of therapy programming, and/or newinsights into therapy's parameters and factors of success.

Using the known conductivity difference between local electrodeimplantation tissue and adjacent fluid media, the method consists oftaking multiple impedance measurements between electrodes with closespacing and electrodes with distant spacing. The difference betweenthese measurements is used to estimate the proximity between the leadand a nearby medium.

FIG. 8 shows a schema of a spinal cord cross section showing the mainstructures. The red arrow with an adjacent ‘d’ represents the distancebetween an implanted SCS lead and the cerebrospinal fluid (CSF). Theblue dotted circle depicts the target of electrical stimulation inspinal cord stimulation therapies.

The position of electrodes implanted in the human body is usuallyassessed by x-ray imaging, and not all tissue structures are visible inthose images (e.g. the epidural fat and the cerebrospinal fluid (CSF) inthe spinal cord are usually not discernable on X-Ray images). As aresult, exact position of electrodes with respect to relevant tissuestructures is usually imprecise. For example, the distance between aspinal cord stimulation (SCS) lead implanted in the epidural fat and theCSF (see FIG. 8 ) is usually not known despite that it plays a role inthe therapy efficiency.

An SCS lead is ideally placed the closest to the CSF so that electricalcurrent can flow through the CSF into the spinal cord (see FIG. 8 ). Butin reality, imaging techniques during lead implant give littleinformation about the distance of the lead from the CSF and the finallead location in the epidural fat can be at various distances from theCSF. This concept can be generalized to any therapy involving a group ofelectrodes on a lead implanted in a resistive tissue that involvesdelivering electrical current to or through a conductive medium.

Electrodes are usually implanted in tissues (e.g. adipose tissue) thathave an electrical conductivity significantly lower than human bodyfluids (e.g. CSF, blood). Impedance measurements between two electrodesare driven by high resistance components. This means that, if there is acomponent with a high impedance followed by a component with highconductivity between two electrodes, the size of that conductivecomponent will have little effect on the overall impedance between thetwo electrodes, because most of the impedance is due to the highlyresistant component. In the example of SCS, the epidural fat between theelectrodes and the CSF drives the overall impedance between twoelectrodes. The extent to which it drives this impedance depends on theactual size of the epidural fat portion, i.e. the distance between theelectrodes and the CSF. This variation can be captured by comparing theimpedance between two adjacent electrodes and two distant electrodes onthe same implanted device.

Embodiment 3

In spinal cord stimulation (SCS), a multi-electrode lead composed of 8cylindrical contacts separated by insulating material is implanted inthe epidural fat. It is connected to a pulse generator implanted in adistal location such as the lower back. It is programmed to deliverelectrical current through the electrodes to stimulate neurons in thespinal cord. The spinal cord where the target neurons are located iscomposed of white and grey matter. It is surrounded by the circulatingCSF contained in the subarachnoid space. That subarachnoid space iswrapped around by the dura mater, a thick tissue layer that separatesthe subdural space from the surrounding epidural fat where the leads areimplanted. The current pathway from electrodes to spinal cord neuronsthus crosses epidural fat tissue, the dura mater and the CSF. Theepidural fat and dura mater have significantly higher resistivity thanCSF. The disclosed method can be applied in this case to giveinformation about the proximity of the lead to the CSF.

A necessary step to carry out the disclosed method is to remove orattenuate the electrode-tissue interface impedance by pre-conditioningthe impedance measurements. To that purpose, a method similar to themethod disclosed in the filed patent application 17.109P-US can beapplied:

-   -   A. Impedance is measured between all possible pairs of        electrodes on the lead (eXeY with X=1, . . . , 8 and Y=1, . . .        , 8 with X #Y in the case of an 8-electrode lead)    -   B. Impedance average ZeX (X=1, . . . , 8) is calculated for each        electrode X across all impedance measurement involving electrode        X    -   C. Impedance average ZeX is removed from each impedance        measurement involving electrode X.

The method consists in calculating the ratio of the impedance betweentwo adjacent electrodes (e1,e2) to the impedance between two mostdistant electrodes (e1,e8) on the same lead, with one common electrode(e1) between the two electrode pairs (see Figure). This ratio variessignificantly according to the distance between the lead and the durabased on the theory described in section 3.1. Note that the thirdelectrode (e8 in this embodiment) does not necessarily have to be thefurthest away from e1, but the further the third electrode, the moreperformant the method. The variation of the ratio with the lead-to-duraCSF has been mathematically modeled with realistic spinal corddimensions and conductivities and is represented in FIG. 10 .

The method comprises the following steps:

-   -   Measure the impedance Ze1e2 between electrode e1 and an adjacent        electrode e2.    -   Measure the impedance Ze1e8 between e1 and e8, the furthest        electrode from e1.    -   Calculate the ratio R=Ze1e2/Ze1e3.    -   Deduce from R the distance between the lead and the CSF:        -   If R is small (R<0.5), then the lead is close to the CSF.        -   If R is large (R>0.5), then the lead is far from the CSF.

FIG. 9 shows a schematic representation of the coronal plan of thespinal cord. Dimensions are not drawn to scale. The impedance Ze1e2between electrode e1 and electrode e2 can be represented by a simplesequence of three resistive components such that Ze1e2=Zef@e1+ZCSF@e1e2+Zef@e2. Likewise, Ze1e8=Zef@e1+ZCSF@e1 e8+Zef@e8. Zef@e1 and Zef@e2represent the impedance of the epidural fat tissue between electrode 1and the CSF, and electrode 2 and the CSF, respectively. ZCSF@e1 e2represents the impedance of the CSF portion between electrode 1 andelectrode 2.

In this specific embodiment, the center-to-center distance between twoelectrodes is 7 mm. The lead-CSF distance is variable but is in therange of hundreds of micrometers to a couple of millimeters. Because ofthat difference in distance, during impedance measurement between twoelectrodes of a lead, the current's least resistive path is to flow intothe CSF, travel in the CSF along the spinal cord and then back into theepidural space to reach the second electrode of the measurement pair, asdepicted in Figure. Note that this is generalizable to any lead withinter-electrode separations significantly larger than lead-to-duradistances.

FIG. 10 shows an estimation of the variation of ratio R according tolead-to-CSF distance using mathematical equations based on the modelillustrated in FIG. 9 and realistic spinal cord dimensions andconductivities.

Embodiment 4

Embodiment 4 is similar to embodiment 3 and uses the same leaddimensions, except that the calculation steps are slightly different: aseries of ratios between impedance measurements of more than two pairsof electrodes are calculated. It is the difference between these ratiosthat depends on the lead proximity to the CSF: the total sum of thecalculated differences greatly increases with the proximity of the leadto the CSF, and vice-versa.

The method comprises the following steps:

-   -   Measure the impedance Ze1eX between electrode e1 and electrode        X, with X=2, . . . , up to the maximum number of electrodes on        the lead (in this embodiment X=2, . . . , 8).    -   Calculate the ratios RX=Ze1e2/Ze1eX, with X=3, . . . , 8.    -   Calculate the differences DY (Y=1, . . . , 5) between        consecutive ratios R4−R3, R5−R4, . . . , R8−R7.    -   Calculate the absolute value of the sum S of all DY (Y=1, . . .        , 5)    -   Deduce from S the distance between the lead and the CSF:        -   If S is small (R<0.5), then the lead is far from the CSF.        -   If S is large (R>0.5), then the lead is close to the CSF.

This embodiment stems from the concept that when the lead is close tothe CSF, the overall impedance will be driven by the CSF impedancecomponent and will therefore increase in a logarithmic fashion withelectrode distance, as illustrated in FIG. 11 . On the opposite, if thelead is far away from the CSF, the overall impedance is driven by theepidural fat and the distance between the electrodes increases theimpedance in a constant manner. This translates in a linear increase ofimpedance with electrode distance, as shown on FIG. 11 .

Thus, the difference between two consecutive ratios is differentdepending on the lead-to-CSF distance: when the lead is close to theCSF, the ratio difference is large between close electrodes, anddecreases with electrode distance, whereas the ratio difference remainssmall when the lead is far away from the CSF. This can be captured bycalculating the absolute value of the sum S of all the ratiodifferences: a small sum reflects little impedance variation acrosselectrode pairs despite the electrode distance, whereas a large sumsuggests high impedance variation across electrode pairs, which meanshigher sensitivity to the distance between electrodes of a pair.

FIG. 11 shows an estimation of the variation of ratio differences Daccording to electrode pair distance, using mathematical equations basedon the model illustrated in FIG. 9 and realistic spinal cord dimensionsand conductivities. When lead-to-CSF distance is 100 micrometers, thearea under the curve (i.e. the value of sum S) is significantly largerthan when the lead-to-CSF distance is 1000 micrometers.

According to an embodiment, to estimate the proximity of a leadimplanted in a medium M1 to a medium M2, the method requires the lead tohave a minimum of 3 separate electrodes of varying length and spacing.

The medium M1 in which the lead is implanted must have a conductivitysignificantly different from the medium M2. The lead, or a systemconnected to the lead, can perform impedance measurements between atleast two pairs of electrodes of the same lead.

The method requires a system that can process (live or offline) basiccalculus operations (sum, difference, division to calculate ratios) andcomparison (superior/inferior) and output the information about leadproximity to the medium M2.

Embodiments of the invention provide a mean to estimate thelead-to-fluid distance in implanted devices, which has currently noknown solutions. It is a rapid (few seconds), easy to implement methodthat requires little computation time and energy to run, and can beapplied to any implanted device that possess multiple electrodes atdifferent distances and that can run impedance measurements, which is acommon feature already implemented in implanted devices.

It will be apparent to those skilled in the art that numerousmodifications and variations of the described examples and embodimentsare possible in light of the above teaching. The disclosed examples andembodiments are presented for purposes of illustration only. Therefore,it is the intent to cover all such modifications and alternateembodiments as may come within the true scope of this invention.

The invention claimed is:
 1. A method for estimating an offset between afirst group and a second group of contacts with respect to alongitudinal direction or a position of a first group of contacts or asecond group of contacts with respect to a longitudinal direction,wherein each group of contacts comprises a plurality of electrodesarranged along a surface of a body of a lead, the method comprising thesteps of: (a) selecting a number N of electrode pairs, each electrodepair including an electrode of the first group of contacts and anelectrode of the second group of contacts, and measuring impedancesbetween the electrodes of each selected electrode pair; (b)pre-conditioning the impedances thus measured for attenuating unwantednoise and to generate pre-conditioned impedances; and (c) determiningthe lead offset or position using the pre-conditioned impedances.
 2. Themethod according to claim 1, wherein the step of pre-conditioning themeasured impedances for attenuating unwanted noise to generatepre-conditioned impedances comprises: calculating for each electrode ofthe second group an average impedance from the measured impedances ofthe electrode pairs including the respective electrode and subtractingthe average impedance from the measured impedances of the electrodepairs that include the respective electrode to obtain processedimpedances; and calculating for each electrode of the first group anaverage processed impedance from the processed impedances of theelectrode pairs including the respective electrode of the first lead andsubtracting the average processed impedance from the processed measuredimpedances of the electrode pairs that include the respective electrodeof the first lead to obtain the pre-conditioned impedances.
 3. Themethod according to claim 1, wherein the number N of selected electrodepairs is equal to or smaller than a number of all possible electrodepairs.
 4. The method according to claim 1, wherein each of theelectrodes of the first group and the second group, respectively, isincluded in the number of selected electrode pairs.
 5. The methodaccording to claim 1, wherein one or more of the following are true:each of the leads comprises 8 electrodes the number N of selectedelectrode pairs equals 32; each of the electrodes of the first and thesecond lead is included in four electrode pairs; the selected electrodepairs are selected such that all electrode offsets between an electrodeof the first lead and an electrode of the second lead are present in arange from −7 to 7 electrodes, the range depending on a total number ofelectrodes and number of electrode pairs respectively.
 6. The methodaccording to claim 1, wherein the method is configured to estimate thelead offset with an accuracy or resolution of less than one electrode,defined by: one width of an electrode in the longitudinal direction plusthe longitudinal distance between the edges of two neighboringelectrodes; or a distance from a center of a width of an electrode to acenter of a width of a neighboring electrode.
 7. The method according toclaim 1, wherein the step of determining the lead offset using thepre-conditioned impedances comprises calculating for each electrodeoffset between an electrode of the first lead and an electrode of thesecond lead an average impedance value corresponding to an average ofthe pre-conditioned impedance values for the respective electrodeoffset.
 8. The method according to claim 7, wherein the step ofdetermining the lead offset further comprises finding a minimumimpedance value among the average pre-conditioned impedance values,wherein the electrode offset corresponding to the minimum impedancevalue is an integer offset, and wherein the lead offset to be determinedis a sum of the integer offset and a fractional offset.
 9. The methodaccording to claim 8, which comprises determining the fractional offsetby extracting two impedance values from average pre-conditionedimpedance values, wherein the two impedance values correspond to twoelectrode offsets neighboring the electrode offset associated with theminimum impedance value.
 10. The method according to claim 1, whereinthe step of determining the lead offset using the pre-conditionedimpedances comprises: calculating for each electrode offset between anelectrode of the first lead and an electrode of the second lead anaverage impedance value corresponding to an average of thepre-conditioned impedance values for the respective electrode offset;and forming a pre-conditioned impedance profile, wherein thepre-conditioned impedance profile comprises the averages of thepre-conditioned impedance values versus the electrode offsets, andwherein a plurality of template profiles is provided, wherein eachtemplate profile corresponds to a detectable lead offset, and includesimpedance values versus lead offset values; and calculating correlationcoefficients between the pre-conditioned impedance profile and all ofthe template profiles, wherein the lead offset is estimated to be thelead offset of the template profile corresponding to a greatestcorrelation coefficient.
 11. A system for estimating a positionalelectrode offset between a first group of electrodes and a second groupof electrodes, the system comprising: a measuring unit for measuringImpedances between the electrodes of a number N of selected electrodepairs; an analyzing unit configured to pre-condition the measuredimpedances; and a calculation unit configured to calculate the electrodeoffset between the group of electrodes using the pre-conditionedimpedances.
 12. The system according to claim 11, wherein thecalculation unit is configured to calculate the electrode offset betweengroups with an accuracy or resolution of less than one distance from acenter of one electrode to a center of at least one second electrode.13. A system for estimating a lead offset between a first lead and asecond lead with respect to a longitudinal direction, along which therespective lead extends, the system comprising: a first lead and asecond lead, each lead including a plurality of electrodes arrangedalong a surface of a body of the respective lead; a measuring unit formeasuring impedances between the electrodes of a number of selectedelectrode pairs, each electrode pair including an electrode of the firstlead and an electrode of the second lead; an analyzing unit configuredto pre-condition the impedances measured by said measuring unit forattenuating unwanted noise and to generate pre-conditioned impedances,said analyzing unit being configured to: calculate for each electrode ofthe second lead an average impedance from the measured impedances of theelectrode pairs containing the electrode and subtracting the averageimpedance from the measured impedances of the electrode pairs containingthe electrode to obtain processed impedances; and calculate for eachelectrode of the first lead an average processed impedance from saidprocessed impedances of the electrode pairs containing the electrode ofthe first lead and subtracting the average processed impedance from theprocessed measured impedances of the electrode pairs containing theelectrode of the first lead to obtain said pre-conditioned impedances;and determine the lead offset using the pre-conditioned impedances.